Efficient Computation of User Optimal Traffic Assignment via Second-Order Cone and Linear Programming Techniques

Wei Wei,Qiuwei Wu,Tao Ding,Longxian Hu

doi:10.1109/access.2019.2942497

Wei Wei, Qiuwei Wu + Show 2 more

Open Access

https://doi.org/10.1109/access.2019.2942497

Copy DOI

Journal: IEEE Access	Publication Date: Jan 1, 2019
Citations: 42	License type: CC BY 4.0

Affiliation: Xi'an Jiaotong University, Tsinghua University

Abstract

Static traffic assignment aims to disclose the spatial distribution of vehicular flow over a transportation network subject to given traffic demands, and plays an essential role in transportation engineering. User-optimal pattern adheres the individual rationality of motorists, in which everyone chooses a route that minimizes his own travel cost, while considering congestion effects influenced by the aggregated movement of vehicles. User optimal traffic assignment, which is also known as the user equilibrium, entails solving an optimization problem with a strictly convex objective function and linear constraints. However, the performances of general-purpose solvers are quite disappointing. This paper proposes two highly efficient computation models for the user equilibrium problem. The first one exploits the second-order cone reformulation of a convex power function, resulting in a second-order cone program, and no approximation is incurred. The second one approximates the convex objective function using a piece-wise linear function, and comes down to a linear program. An adaptive path generation oracle is devised in order to circumvent path enumeration in problem setup. Case studies demonstrate that the proposed method can deal with large-scale transportation systems, and outperforms the most popular iterative algorithm in the literature.

Highlights

The traffic assignment problem (TAP) is a fundamental problem in transportation engineering and underlies many practical applications such as network topology design, road capacity expansion planning, and traffic signal control
This paper focuses on the fundamental UE problem, and aims to fill the gap between the UE computation and highly efficient algorithms for conic and linear programs
TAP is formulated as a convex optimization problem, we find in experiments that general-purpose solvers, no matter interior-point algorithm based ones or sequential quadratic programming based ones, can only solve small-scale instances, unlike the state-of-the-art linear program (LP) solver which can cope with problems with hundreds of thousands of variables

Summary

INTRODUCTION

The traffic assignment problem (TAP) is a fundamental problem in transportation engineering and underlies many practical applications such as network topology design, road capacity expansion planning, and traffic signal control. EFFICIENT COMPUTATION MODELS problem (6) is convex, the worst-case complexity of the interior-point algorithm for finding a ε-optimal solution of a general convex program turns out to be [37]. O(1)n n3 + M ln 1 ε where n is the number of variables; at any given point, the values of functions in the objective and constraints together with their derivatives can be computed using M arithmetic operations This bound is already unacceptable for n with an order of magnitude of 103. The piecewise linear approximation approach does not rely on any specific structure of the latency function ta(xa) As long as it is increasing, such as the Davidson function in [43] which considers a mandatory upper bound of traffic flow, FIGURE 2. Its integral is convex in xa, and this approach remains valid

AN ADAPTIVE PATH GENERATION ORACLE

CASE STUDIES

SIOUX FALLS NETWORK

Findings

CONCLUSION